# Numerical Simulation of the Application of Solar Radiant Systems, Internal Airflow and Occupants’ Presence in the Improvement of Comfort in Winter Conditions

^{*}

## Abstract

**:**

_{2}concentration is numerically calculated. In the validation tests, the experimental and numerical values of the chamber surface temperature, the air temperature, the air velocity, the air turbulence intensity and the DR are presented.

## 1. Introduction

_{2}) concentration field, around the occupant and inside the chamber space. The BTR numerical model evaluated the transparent surfaces’ temperatures, opaque surfaces’ temperatures, internal air temperatures, solar collectors’ temperatures and duct water temperature. In the experimental methodology, the air velocity and the air temperature fluctuation around the 15 human body sections (used to evaluate the local thermal discomfort level and to validate the numerical values) and the surrounding chamber surface temperature are measured.

_{2}concentration, evaluated by the CFD numerical model, is used as an indicator of the indoor air quality. The CO

_{2}concentration, used in this work, is released by the occupants. In this work, the recommendations of [25,26] are used. Some examples of the application of CO

_{2}concentration can be seen, for example, in [27,28,29,30]. In [27], a study of CO

_{2}dispersion in an auditorium is developed, and in [28], a work of indoor air quality in school buildings is presented; while in [29], the CO

_{2}concentration in the airflow pattern in a residential building is used, and in [30], the CO

_{2}concentration is used in the evaluation of the outdoor air ventilation rates.

## 2. Numerical Model

_{2}concentration); while the BTR integral numerical model approach is used to evaluate the transparent surfaces’ temperatures, opaque surfaces’ temperatures, internal air temperatures, solar collectors’ temperatures and duct water temperature.

- In the first step, the BTR numerical model calculated the chamber surrounding temperatures, using the external and internal environment conditions;
- In the second step, the human thermal comfort numerical model calculated the body and clothing temperatures, using the chamber surrounding temperatures and occupant surrounding environments variables;
- In the third step, the CFD numerical model, using the previous values (skin, clothing and chamber temperatures), calculated the airflow around the occupants.

#### 2.1. Human Thermal Comfort Numerical Model

- Body (tissue temperature);
- Blood (arterial and venous temperature);
- Skin (water vapor);
- Clothing (layers’ temperature);
- Clothing (layers’ water vapor);
- Thermal comfort level (PMV and PPD indexes).

- Surrounding air temperature and velocity (calculated by the CFD numerical model);
- Air relative humidity;
- Surrounding surface (walls, floor, window, door, roof and desk temperatures), calculated by the BTR numerical model;
- Internal sources (computers and others);
- Occupants (height, weight, activity level and clothing level).

#### 2.2. Computational Fluid Dynamics Numerical Model

- Three-dimensional components of air velocity;
- Omnidirectional air velocity;
- Air temperature;
- Air pressure;
- Turbulent kinetic energy;
- Turbulent energy dissipation rate;
- Carbon dioxide concentration;
- Local thermal discomfort level;
- Air quality level.

- Surrounding surfaces variables (windows, walls, ceiling, floor and desk temperature), calculated by the BTR numerical model;
- Occupants’ presence (human and clothing temperature), calculated by the HTC numerical model);
- Occupants’ respiration (carbon dioxide concentration release);
- Inlet air flow (air velocity, carbon dioxide concentration, air temperature and turbulence intensity).

#### 2.3. Building Thermal Response Numerical Model

- Walls (indoor, central and outdoor layers’ temperature);
- Floor (wood, cement, water and isolation layers’ temperature);
- Windows (glass temperature);
- Door (indoor, central and outdoor layers’ temperature);
- Roof (indoor, central and outdoor layers’ temperature);
- Desk (indoor body);
- Solar collector (outlet water temperature);
- Solar collector ducts (inlet water and duct temperature).

- Collector solar radiation (incident solar radiation);
- External conditions (air temperature and air relative humidity);
- Occupants (height, weight, activity level and clothing level).

## 3. Experimental Setup

^{3}) equipped with one desk, two seats, two seated hygro-thermal manikins, a warm radiant floor, a solar radiation simulator, a water solar collector and two indoor climate analyzers are used in the experimental setup. In the radiant floor, a solar radiation simulator and a water solar collector are used (see more details in Figure 1).

## 4. Numerical Methodology

## 5. Results and Discussion

- in the first section, the surrounding chamber surfaces’ temperatures are analyzed;
- in the second section, the air velocity and the air temperature field inside the space are analyzed;
- in the third section, the air velocity, the air temperature, the MRT and the thermal comfort level are presented;
- in the fourth section, the air turbulence intensity and the DR are discussed;
- in the fourth section, the CO
_{2}concentration is shown.

#### 5.1. Chamber Surrounding Temperatures

#### 5.2. Air Flow inside the Chamber Space

- a horizontal airflow to the upper area;
- a vertical descendent airflow to the lower occupied area.

#### 5.3. Thermal Comfort Level

#### 5.4. Local Thermal Discomfort

#### 5.5. Air Quality

_{2}concentration is numerically analyzed. In Figure 11, the CO

_{2}concentration field in the horizontal plan, in the respiration area, is presented, while in Table 6, the CO

_{2}concentration is presented. In both situations, for both occupants, the calculated CO

_{2}concentration is obtained in front of the nose area.

_{2}concentration inside the space, in general, is higher in the breathing area of the occupants and is reduced when the distance with the breathing area increases. In general, with the exception to some centimeters’ distanced from the breathing area, the carbon concentration inside the space is around of 500 mg/m

^{3}.

_{2}concentration, in the numerical simulation, the values are slightly different when the RNG and the k-epsilon turbulence models are used.

_{2}concentration than the left side seated occupant. These results are associated with the airflow trajectory, from the occupant seated in the left side area to the outlet.

## 6. Conclusions

_{2}concentration than the left side seated occupant.

_{2}concentration in the breathing area when the k-epsilon turbulence model is used is 1557 mg/m

^{3}, and when the RNG turbulence model is used, it is 1409 mg/m

^{3}. Thus, in accordance with the obtained values, the thermal comfort level is acceptable, the local thermal discomfort level is not acceptable and the air quality level is acceptable.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) Chamber, water ducts and collector scheme used in the building thermal response (BTR) numerical model; (

**b**) occupants, interior bodies and chamber schemes used in the human thermal comfort (HTC) numerical model; (

**c**) occupants, interior bodies and plans located at Y = 110 cm (Y22), Y = 170 cm (Y34), X = 130 cm (X23) and Z = 120 cm (Z23), used by the CFD numerical model in the work.

**Figure 2.**Air velocity (

**a1,a2**) and air temperature (

**b1,b2**) fields in the plan located at Y = 110 cm (Y22) (right side seated occupant), numerically calculated. (

**a1,b1**) are associated with the k-epsilon turbulence model, and (

**a2,b2**) are associated with the RNG turbulence model.

**Figure 3.**Air velocity (

**a1,a2**) and air temperature (

**b1,b2**) fields in the plan located at Y = 170 cm (Y34) (left side seated occupant), numerically calculated. (

**a1,b1**) are associated with the k-epsilon turbulence model, and (

**a2,b2**) are associated with the RNG turbulence model.

**Figure 4.**Air velocity (

**a1,a2**) and air temperature (

**b1,b2**) fields in the plan located at X = 130 cm (X23), numerically calculated. (

**a1,b1**) are associated with the k-epsilon turbulence model, and (

**a2,b2**) are associated with the RNG turbulence model.

**Figure 5.**Air velocity (

**a1,a2**) and air temperature (

**b1,b2**) fields in the plan located at Z = 120 cm (Z23), numerically calculated. (

**a1,b1**) are associated with the k-epsilon turbulence model, and (

**a2,b2**) are associated with the RNG turbulence model.

**Figure 6.**Air velocity value around the occupants seated on the right and left side, numerically calculated and experimentally measured. In (

**a**), the k-epsilon turbulence model is used, and in (

**b**), the RNG turbulence model is applied.

**Figure 7.**Air temperature values around the occupants seated on the right and left side, numerically calculated and experimentally measured. In (

**a**), the k-epsilon turbulence model is used, and in (

**b**), the RNG turbulence model is applied.

**Figure 8.**Numerical mean radiant temperature (MRT) values around the occupants seated on the right and left side are subjected.

**Figure 9.**Air turbulence intensity (TI) around the occupants, numerically calculated and experimentally measured. In (

**a**), the k-epsilon turbulence model is used, and in (

**b**), the RNG turbulence model is applied.

**Figure 10.**Draught risk (DR) around the occupants numerically calculated and experimentally measured. In (

**a**), the k-epsilon turbulence model is used, and in (

**b**), the RNG turbulence model is applied.

**Figure 11.**CO

_{2}concentration field for the plan XY, Z23, numerically calculated. (

**a**) Associated with the k-epsilon turbulence model and (

**b**) associated with the RNG turbulence model.

Variables | Measured Values |
---|---|

Inlet air velocity | 3.9 m/s |

Inlet air temperature | 17.6 °C |

Inlet air turbulence | 6% |

Solar radiation | 750 W/m^{2} |

Collector area | 2 m^{2} |

Water mass flow | 0.24 kg/s |

Variables | Measurements |

Chamber surfaces temperatures | Floor, ceiling, wall and interior bodies temperature |

Air velocity | Around 15 human body sections |

Air temperature | Around 15 human body sections |

Variables | Measured Values | CALCULATED VALUES |
---|---|---|

Floor temperature | 28.3 °C | 28.45 °C |

Ceiling temperature | 18.5 °C | 19.14 °C |

Wall temperature | 18.0 °C | 19.17 °C |

Interior bodies temperature (desk) | 18.0 °C | 19.39 °C |

**Table 3.**Air velocity and the temperature accuracy obtained in the validation tests using the k-epsilon and RNG turbulence models.

Situation | Model | |
---|---|---|

k-epsilon | RNG | |

Air velocity around the right side occupant | 0.8372 | 0.8777 |

Air velocity around the left side occupant | 0.8511 | 0.9119 |

Air temperature around the right side occupant | 0.9963 | 0.9966 |

Air temperature around the left side occupant | 0.9961 | 0.9965 |

**Table 4.**Predicted mean vote (PMV) and percentage of dissatisfied people (PPD) indexes numerically calculated.

k-epsilon | RNG | |||
---|---|---|---|---|

PMV | PPD (%) | PMV | PPD (%) | |

Right side seated occupant | −0.59 | 12.2 | −0.73 | 16.3 |

Left side seated occupant | −0.57 | 11.9 | −0.71 | 15.6 |

**Table 5.**Air turbulence intensity and DR accuracy obtained in the validations tests using the k-epsilon and RNG turbulence models.

Situation | Model | |
---|---|---|

k-epsilon | RNG | |

Air turbulence intensity around the right side occupant | 0.9836 | 0.9942 |

Air turbulence intensity around the left side occupant | 0.9891 | 0.9973 |

DR around the right side occupant | 0.9886 | 0.9965 |

DR around the left side occupant | 0.9884 | 0.9976 |

CO_{2} Concentration (mg/m^{3}) | k-epsilon | RNG |
---|---|---|

Right side seated occupant | 971 | 1105 |

Left side seated occupant | 2143 | 1713 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Conceição, E.Z.E.; Lúcio, M.M.J.R.
Numerical Simulation of the Application of Solar Radiant Systems, Internal Airflow and Occupants’ Presence in the Improvement of Comfort in Winter Conditions. *Buildings* **2016**, *6*, 38.
https://doi.org/10.3390/buildings6030038

**AMA Style**

Conceição EZE, Lúcio MMJR.
Numerical Simulation of the Application of Solar Radiant Systems, Internal Airflow and Occupants’ Presence in the Improvement of Comfort in Winter Conditions. *Buildings*. 2016; 6(3):38.
https://doi.org/10.3390/buildings6030038

**Chicago/Turabian Style**

Conceição, Eusébio Z. E., and Mª Manuela J. R. Lúcio.
2016. "Numerical Simulation of the Application of Solar Radiant Systems, Internal Airflow and Occupants’ Presence in the Improvement of Comfort in Winter Conditions" *Buildings* 6, no. 3: 38.
https://doi.org/10.3390/buildings6030038